Mayor Bill de Blasio issued an unusual and stern rebuke of New York City’s tabloid newspapers on Monday, calling on them to apologize for publishing front-page headlines that suggested his wife, Chirlane McCray, had admitted to being a reluctant mother to the couple’s daughter, Chiara.

The mayor’s remarks — he called the coverage “disturbing and inappropriate” — were primarily directed at The New York Post, which featured a front-page photograph of Ms. McCray next to a headline, in two-inch type: “I Was a Bad Mom!”